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Volumn 68, Issue 2, 2003, Pages 9-

Statistical mechanical approaches to models with many poorly known parameters

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[No Author keywords available]

Indexed keywords


EID: 85035221677     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.68.021904     Document Type: Article
Times cited : (109)

References (37)
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    • We have tried to find the appropriate attribution for this quote but have been unsuccessful. Variants of the statement (differing in the number of parameters) have been attributed to C.F. Gauss, Niels Bohr, Lord Kelvin, Enrico Fermi, and Richard Feynman
    • We have tried to find the appropriate attribution for this quote but have been unsuccessful. Variants of the statement (differing in the number of parameters) have been attributed to C.F. Gauss, Niels Bohr, Lord Kelvin, Enrico Fermi, and Richard Feynman.
  • 11
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    • K.S. Brown, C.C. Hill, G.A. Calero, K.H. Lee, J.P. Sethna, and R.A. Cerione (unpublished)
    • K.S. Brown, C.C. Hill, G.A. Calero, K.H. Lee, J.P. Sethna, and R.A. Cerione (unpublished).
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    • C.C. Hill and J.P. Sethna (unpublished)
    • C.C. Hill and J.P. Sethna (unpublished).
  • 19
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    • our real system we had no data for the PI3K loop and used methods described in this manuscript to determine if the loop should be included given the data. Thus, for the “perfect” model we generated no data for this loop in order to use the model as a test case for the model selection methods, as we used it as a test case for other methods. However, the perfect model is unenlightening in this respect because model selection methods in a sense tell us what we already know, i.e., that the loop was present when the data were generated and are hence necessary
    • In our real system we had no data for the PI3K loop and used methods described in this manuscript to determine if the loop should be included given the data. Thus, for the “perfect” model we generated no data for this loop in order to use the model as a test case for the model selection methods, as we used it as a test case for other methods. However, the perfect model is unenlightening in this respect because model selection methods in a sense tell us what we already know, i.e., that the loop was present when the data were generated and are hence necessary.
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    • R. Fletcher, Practical Methods of Optimization, 2nd ed. (Wiley, Chichester, 1987)
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    • Our methods identify typical, but not all, members of the ensemble. New data outside the error bars may, in principle, be consistent with the existing model but restrict the parameters to a formerly insignificant subregion
    • Our methods identify typical, but not all, members of the ensemble. New data outside the error bars may, in principle, be consistent with the existing model but restrict the parameters to a formerly insignificant subregion.
  • 23
    • 85035236880 scopus 로고    scopus 로고
    • The prior distribution is flat in the (Formula presented) and in the parameters (logs of the rate constants). Using such a deceptively simple prior (equivalent, at least for the rate constants, to a Jeffrys prior) can have more subtle and serious consequences than one might think. For more details, see the model selection section and references therein. The (Formula presented) are quadratic in the cost and can be integrated out of the partition function (see text); they play the role of uninteresting “nuisance parameters” in the Bayesian language
    • The prior distribution is flat in the (Formula presented) and in the parameters (logs of the rate constants). Using such a deceptively simple prior (equivalent, at least for the rate constants, to a Jeffrys prior) can have more subtle and serious consequences than one might think. For more details, see the model selection section and references therein. The (Formula presented) are quadratic in the cost and can be integrated out of the partition function (see text); they play the role of uninteresting “nuisance parameters” in the Bayesian language.
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    • I.T. Jolliffe, Principal Component Analysis (Springer-Verlag, New York, 1986)
    • I.T. Jolliffe, Principal Component Analysis (Springer-Verlag, New York, 1986).
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    • W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, New York, 1996)
    • W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, New York, 1996).
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    • M.E.J. Newman and G.T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, New York, 1999)
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    • M.P. Nightingale and C.J. Umrigar (unpublished)
    • M.P. Nightingale and C.J. Umrigar (unpublished).
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    • C. Lanczos, Applied Analysis (Prentice Hall, Englewood Cliffs, NJ, 1956)
    • C. Lanczos, Applied Analysis (Prentice Hall, Englewood Cliffs, NJ, 1956).
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    • S.J. Press, Bayesian Statistics: Principles, Models, and Applications (Wiley, New York, 1989)
    • S.J. Press, Bayesian Statistics: Principles, Models, and Applications (Wiley, New York, 1989).
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    • H. Akaike, in 2nd International Symposium on Information Theory, edited by B.N. Petrov and F. Csaki (Akademia Kiado, Budapest, 1973), pp. 267–281
    • H. Akaike, in 2nd International Symposium on Information Theory, edited by B.N. Petrov and F. Csaki (Akademia Kiado, Budapest, 1973), pp. 267–281.


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